Question

Find a quadratic polynomial the sum and products of whose zeros are 0 and -root2 respectively.

Answer 1

Let à and ß be the zeroes of the polynomial.

Sum of zeroes = (à+ß) = 0

Product of zeroes = (àß) = -√2

The quadratic polynomial is in the form of

x²-(à+ß)x+(àß)

→ x²-(0)x+(-√2)

→ x²-√2

Hope it helps...

Answer 2

Hey there !!!!!

P(x)=ax²+bx+c is a polynomial whose zeroes are α,β

P(x) in terms of α,β can be expressed as 

P(x)=ax²-(α+β)x+(αβ)

Given that α+β=0 αβ=-√2

P(x)= x²-√2.